Neither daylight nor darkness is dispelled.

Under the entry for darkness in the Player's Handbook, we see:

If any of this spell’s area overlaps with an area of light created by a spell of 2nd level or lower, the spell that created the light is dispelled.

And under the entry for daylight in the Player's Handbook, we see a similar:

If any of this spell’s area overlaps with an area of darkness created by a spell of 3rd level or lower, the spell that created the darkness is dispelled.

Neither of these spells contain an "At Higher Levels" clause allowing them to dispel higher leveled opposing luminosity spells, so casting them at higher levels only protects them from being dispelled.

So, we know they don't dispel one another, but as you've asked, what exactly happens in the space where the spells overlap?

Daylight prevails.

Again, under the entry for darkness in the Player's Handbook, we see:

A creature with darkvision can’t see through this darkness, and nonmagical light can’t illuminate it.

Daylight is certainly magical light, so it is not hindered by darkness.

Similarly, continual flame can be cast from a 3rd level spell slot to create a torch whose light pierces magical darkness.

No. There is specific sage advice on the matter:

@JeremyECrawford like most spells can a known cantrip be cast at a higher spell slot lvl. Aka sacred flame lvl 1 for 2d8 radiant dmg
— redwoodguardian (@redwoodguardian) August 24, 2015

No, since cantrips don't use spell slots. https://t.co/MKpg8oozyf
— Jeremy Crawford (@JeremyECrawford) August 24, 2015